A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $9$ and the height of the cylinder is $12$ . If the volume of the solid is $72 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-12-22T13:18:04

Area of the base of the cylinder is 15.0796

Let V be the volume of the solid = $72 pi$

Volume of the object V = volume of cylinder + volume of cone

Given cylinder height $h = 12$ , cone height $H = 9$

Volume of cylinder $= pi * r^2 * h$

Volume of cone $= (1/3) pi * r^2 * H$

$V = pi r^2 h + (1/3) pi r^2 H$

$96 pi = pi r^2 (h + (1/3)H)$

$r^2 = (72 cancel(pi)) / (cancel(pi) (12 + (1/3)9))$

$r^2 = 72/15$

Area of base of cylinder $A = pi r^2 = pi * (72/15) = 15.0796$

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 9 9 and the height of the cylinder is 12 12 . If the volume of the solid is 72 pi72 pi, what is the area of the base of the cylinder?